Reference ID: MET-D0F3 | Process Engineering Reference Sheets Calculation Guide
Introduction & Context
Radial-flow impellers are the work-horse of mechanically agitated gas–liquid contactors in the process industries.
Selecting the correct impeller diameter and rotational speed for a given vessel geometry, fluid properties and
aeration rate is a prerequisite for achieving the desired mass-transfer performance while avoiding mechanical or
operational problems such as gas flooding or excessive shear. The short design sheet reproduced here implements the
classical power-number approach for a six-blade Rushton turbine (power number Po = 5) and checks
the resulting Reynolds number, tip speed and dimensionless aeration number to ensure that the chosen operating
point lies within the turbulent, well-dispersed regime.
Methodology & Formulas
Convert practical inputs to SI units
Dynamic viscosity: \( \mu \,[\text{Pa·s}] = \mu_{\text{cP}} / 1000 \)
Absolute pressure: \( P_{\text{abs}} \,[\text{Pa}] = P_{\text{bar}} \times 10^{5} \)
Impeller diameter: \( d = (d/T)\,T \)
Rotational speed: \( N \,[\text{s}^{-1}] = N_{\text{rpm}} / 60 \)
Reynolds number
\[ Re = \frac{ \rho\,N\,d^{2} }{ \mu } \]
Flow regime
Re range
Laminar
Re < 10
Transition
10 ≤ Re < 10,000
Turbulent (Rushton)
10,000 ≤ Re ≤ 1,000,000
Power draw
Target power: \( P = P_{\text{spec}} \cdot V_{\text{liq}} \)
Power number check: \( P_{o} = \frac{ P }{ \rho\,N^{3}\,d^{5} } \)
Tip speed (shear indicator)
\[ v_{\text{tip}} = \pi\,N\,d \]
Radial-flow impellers are the best choice when you need high shear, rapid heat or mass transfer, or when the process fluid viscosity is above ~10,000 cP. Typical applications include gas dispersion, immiscible liquid mixing, and fast chemical reactions. Select radial flow when:
The Reynolds number is below 10 indicating laminar or transitional flow
Power draw must remain nearly constant as viscosity rises
Short blend or reaction times (<2 min) are critical
Bottom uniformity is less important than local turbulence
Use the power number (Np) curve for your specific impeller style. For a flat-blade Rushton turbine in turbulent water, Np ≈ 5. The steps are:
Fix tip speed 3–6 m s⁻¹ for shear-sensitive systems or 6–10 m s⁻¹ for dispersion
Calculate diameter D = (tip speed × 60) / (π N) where N is rpm
Compute Reynolds number Re = (ρ N D²) / μ
Read actual Np from curve at that Re
Power P = Np ρ N³ D⁵; scale-up using constant P/V if reaction time dominates or constant tip speed if shear governs
Radial impellers create high unbalanced hydraulic forces that shorten gear-box and shaft life. Mitigate these by:
Limiting blade length to ≤ ⅓ tank diameter to reduce shaft deflection
Using steady bearings or bottom support when shaft length-to-diameter ratio exceeds 35
Specifying a critical speed margin ≥ 1.8× operating speed to avoid resonance
Selecting duplex angular-contact bearings in the gearbox to handle the large axial load reversal during start-up
Gas handling capacity (QG) and mass-transfer coefficient kLa depend on impeller style. For a Rushton turbine:
Flooding occurs when QG > 0.025 N D³; switch to a concave-blade or super-single design to raise flooding limit by 30–50%
kLa scales with (P/V)0.7 (QG/V)0.3; increasing blade width from T/5 to T/4 doubles power and raises kLa ~60%
Sparger ring diameter should be 0.8 D to minimize gas bypass through the hub vortex
Worked Example – Selecting a Rushton Impeller for a 6 m³ Aerobic Fermenter
A process engineer must verify that a 0.66 m diameter Rushton turbine can deliver 1 kW·m⁻³ of specific power in a 6 m³ working volume while keeping the tip speed below 5 m·s⁻¹. The broth is a Newtonian fluid (ρ = 1020 kg·m⁻³, μ = 2.5 cP) and is sparged at 1.67 L·s⁻¹ (1 vvm). The vessel is 2 m in diameter and 2 m straight-side, giving a 2 m liquid height.
Knowns
Working volume, V = 6 m³
Tank diameter, T = 2 m
Liquid height, H = 2 m
Impeller-to-tank ratio, d/T = 0.33 → d = 0.66 m
Impeller speed, N = 120 rpm = 2 s⁻¹
Fluid density, ρ = 1020 kg·m⁻³
Fluid viscosity, μ = 2.5 cP = 0.0025 Pa·s
Gas flow rate, Qg = 1.67 L·s⁻¹ = 0.00167 m³·s⁻¹
Target specific power, P/V = 1 kW·m⁻³ = 1000 W·m⁻³
Maximum allowable tip speed, vtip,max = 5 m·s⁻¹
Power number for Rushton turbine, Po ≈ 5 (ungassed)
Step-by-step calculation
Reynolds number
\[
Re = \frac{\rho N d^{2}}{\mu} = \frac{1020 \times 2 \times 0.66^{2}}{0.0025} = 355\,450
\]
Since Re > 10,000, the flow is fully turbulent and the constant power-number assumption is valid.
Specific power
\[
\frac{P}{V} = \frac{6000}{6} = 1.0 \text{ kW·m}^{-3}
\]
This matches the target exactly.
Tip speed
\[
v_{\text{tip}} = \pi N d = \pi \times 2 \times 0.66 = 4.15 \text{ m·s}^{-1}
\]
4.15 m·s⁻¹ < 5 m·s⁻¹ → acceptable.
Gassed power check
Flooding number
\[
Fl_{g} = \frac{Q_{g}}{N d^{3}} = \frac{0.00167}{2 \times 0.66^{3}} = 0.0029
\]
For a Rushton turbine at this low gas rate the power reduction is <10%; the ungassed value is therefore conservative and still meets the 1 kW·m⁻³ requirement.
Final Answer
A 0.66 m Rushton turbine running at 120 rpm (2 s⁻¹) supplies 6 kW of power, achieving the desired 1 kW·m⁻³ specific power with a tip speed of 4.15 m·s⁻¹, safely below the 5 m·s⁻¹ limit. The impeller is therefore suitable for this duty.
"Un projet n'est jamais trop grand s'il est bien conçu."— André Citroën
"La difficulté attire l'homme de caractère, car c'est en l'étreignant qu'il se réalise."— Charles de Gaulle
